Why is Spain and Italy’s youth unemployment still so high?

I can answer for Italy alone, as I do not have any knowledge of the Spanish economic fabric.

Regarding the stubbornly high youth unemployment rate in Italy (now back above 40%, as of January 2017 and it has been hovering above 35% since 2009), there are multiple reasons behind it:

A. The Italian State genuinely hates entrepreneurs: it is basically impossible to do business in Italy. Those doing a business in Italy should be considered modern heroes, in my opinion. There is a constellation of bureaucratic hurdles, notaries, accountants, lawyers, whatever, that you are forced by the law to consult (and pay hefty fees) even BEFORE you start a business. After you start it, there will be a multitude of completely irrational tax deadlines with draconian penalties (that change every year), bureaucratic checks, useless controls, etc. that actively make your business frankly impossible. Bureaucrats live in medieval times, detached from reality, and they hate businessmen & risk-takers.

B. Lack of financial credit. Italy lacks a modern and efficient banking system. Money is lent by banks to friends, friends of friends, relatives of friends, etc. This approach proved disastrous and was able to take very important financial institutions (like Monte dei Paschi di Siena, the 3rd largest bank in Italy and Banca Popolare di Vicenza) to collapse because of Non Performing Loans generated by a handful (0.01%) of clients.

C. Closed market sectors: this is the elephant hiding behind the curtains of the room. In Italy entire market sectors are purposely closed to competitors (i.e. newcomers) in order to maintain the good life of the incumbents. Nobody is willing to touch the incumbents’ privileges because any action against them would be politically very pricey. Pharmacists, Notaries, University Professors, Taxi Drivers, etc. are just a few examples of ferocious pressure groups that have been able to blackmail and eventually force the legislator for decades to prevent by the law any innovation in their relevant sectors so to close their markets to any potential competition. Many excellent Pharmacy Graduates, Law Graduates, or would-be Taxi Drivers (these are just examples) are not able to enter the market and do their job because there is an artificial limit legally set forth by the State to the lucky few “members” who are allowed to practice that profession. Regardless how high is the youth unemployment rate, the legislator will not open these markets to new players as the existent ones would have to face new competition (and, potentially, compressed profits).

D. Secondary school system (particularly Universities) is totally detached from reality, living in a universe where the actual job you will be asked to do is completely irrelevant. After the students will graduate, they will not have acquired any set of skills useful in the market. Once you will have spent 4–6 years to get a degree, you will need to start from scratch to learn the skills needed in the market. (I have been suggested by Luca Accomazzi that this situation is currently improving).

E. As other answers here have already stated, the judiciary system in Italy is purposely archaic and inefficient: if you need to recover a debt, be ready to wait years while you carry out expensive litigation, and the result is far for certain thanks to the many loopholes that Italian lawyers are able to exploit to delay and eventually avoid to repay their clients’ debts.